The sensitivity of the β-material parameter and its determination based on optimization of error in the mechanical properties

The β-material is an extremely useful parameter for the analysis of nanoindentation data as it correlates different nanomechanical quantities and greatly simplifies the conventional Oliver and Pharr method used for determination of mechanical properties. Primarily, it may be determined both by fitting several sets of experimental data relating two nanomechanical quantities and from the total energy dissipated during indentation. While the first method is very cumbersome, the second may yield erroneous value for some materials. Reexamination of the experimental data on three ceramics available in the literature reveals that this parameter is very sensitive. Even a small error in its approximation may lead to a substantial error in the computation of initial unloading stiffness, contact area, elastic modulus and hardness values in certain conditions, and therefore, it must be determined very precisely. In this paper, a method for the determination of the β-material parameter based on the optimization of error in mechanical properties is proposed. β determined using the proposed technique not only ensures the goodness of fit to the experimental data but also satisfies the loop conditions more precisely.